Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation

2025/04/26 by Li, Shi-Hao, Tsujimoto, Satoshi, Watanabe, Ryoto +1 · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.18891

Abstract

This paper intends to construct discrete spectral transformations for Cauchy-Jacobi orthogonal polynomials, and find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy-Jacobi orthogonal polynomials acts as the τ-function of the discrete CKP equation, which has applications in Yang-Baxter equation, integrable geometry, cluster algebra, and so on.

Cited by

• Elliptic solutions of the lattice CKP equation and its elliptic direct linearisation scheme

Related

• Pearson Equations for Discrete Orthogonal Polynomials: I. Generalized Hypergeometric Functions and Toda Equations
• Discrete harmonic analysis associated with Jacobi expansions I: the heat\n semigroup
• The search for differential equations for orthogonal polynomials by using computers
• On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
• The search for differential equations for certain sets of orthogonal polynomials